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ALBANY – The state’s cost to give a $350 tax break to some middle-class taxpayers and to cover part of the higher payroll costs for businesses under the new minimum wage hike program will be more than the amount predicted last week by state officials.

The $350 tax break – in the form of checks to be delivered to a million or so taxpayers just before the November 2014 election – is now projected to cost the state $410 million. That is up from the $350 million to $375 million officials estimated a week ago.

That tax break will go to households with at least one dependent child and adjusted gross incomes between $40,000 and $300,000. Critics have questioned the logic behind calling such a family making $300,000 middle class and say it discriminates against couples without children and lower-income families.

The state-funded minimum wage subsidy will go to businesses to cover the difference when the minimum wage goes from $7.25 to $8 per hour in January. The 75 cents per hour subsidy will cover the costs for businesses that employ 16- to 19-year-olds who are students, though the budget bill does not define “student.” When the wage is raised to $9 in January 2016, the state will pay businesses $1.35 per hour per employee for every one of those eligible workers. Backers say it will help smooth the costs for employers to avoid worker layoffs; critics say it is an unfair subsidy that will encourage companies to hire teens over workers age 20 and above, including senior citizens who can’t afford to live just on Social Security.

The minimum wage tax subsidy was to cost about the state $45 million per year, officials said. New numbers from the Cuomo administration now show the subsidy will cost $35 million in the 2015 tax year and then average $65 million in each of the following three years.

Gov. Andrew M. Cuomo is scheduled to visit the South Campus of the University at Buffalo at 10:30 a.m. today. His visit had been scheduled for Monday, but was postponed.